Can a Program be Wrong?

For full discretion, I'm not a programmer, and I don't know anything about programs or software. I'm a photographer. But I have a question, and hope all of you will be kind enough to forgive this post its flaws, and generous enough to help me with an answer.

Can a website that processes information, such as an online library book renewal system, say that it's processed your request, but not actually do it? Specifically, a few days ago I remember renewing books at Santa Clara City Library [link=]([/link] under the "My Account" section of the site, but today it charged me for not renewing them. I have a specific memory of checking the boxes to renew the books.

The idea that is commonly carried among lay people, I think, is that computers and programs are infallible. Is it possible for any reason you can think of, that this website made a mistake? If so, can you list a few possibilities of why and how it could make an error?

Thanks for your help.
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